Persistence modules are objects used in Topological Data Analysis to extract algebraic summaries about the topology of data. Typically, persistence modules are obtained from datasets endowed with measurements. As data are discrete, without loss of generality, we can use elements of \(\mathbb {Z}^n\)  (\(n\ge 1\) ) to encode the values of \(n\)  measurements. Filtering the given data according to increasing values of the measurements (in the coordinate-wise partial order of \(\mathbb {Z}^n\) ), and applying homology, one obtains the corresponding \(n\) -parameter persistence module [1]}.
